A common solution to the board flex problem is to stick on rubber bumpers on the back side of the board to fill in the space behind the board up to the enclosure wall. This way when you push on the connectors the board will not flex nearly as much.

Do use care to select rubber feet that have an adhesive that have a known chemical makeup. I have seen at least one instance where such bumpers were used where the adhesive contained some acidic component. Over time the fan driven airflow over the board spread the out gassing chemicals from the bumper adhesive downwind on the board and caused some copper corrosion on the exposed edges of pads and vias.